Topology optimization using fully adaptive truncated hierarchical B-splines

In this work, we propose a topology optimization (TO) method using fully adaptive truncated hierarchical B-splines (ATHB-TO), where the adaptive isogeometric analysis mesh and design mesh of ATHB-TO are locally refined and coarsened simultaneously. To meet the demands of full-mesh adaptivity of ATHB-TO, a marking strategy is established based on density variances between adjacent active elements. Then, an adaptive formulation for the mark strategy is proposed to avoid the overrefinement phenomenon that occurred in the adaptive TO method using a fixed mark strategy. Moreover, a density inheritance strategy is devised to project original design variables into design variables concerning a fully adaptive hierarchical mesh. Afterward, ATHB-TO with an adaptive mark strategy is successfully applied to two-dimensional and three-dimensional benchmarks. Numerical results show that the ATHB-TO method can obtain identical optimized designs at a lower computational burden, and improve the convergence rate compared with THB-TO with only hierarchical local refinement considered. Adopting the adaptive mark strategy releases the full potential of ATHB-TO in improving the computational efficiency compared with the fixed mark strategy. Additionally, the adaptive TO schemes outperform TO performed on uniformly refined meshes due to the enhanced numerical efficiency and improved structural performance with a largely accelerated convergence rate. Therefore, ATHB-TO is an effective way of solving structural TO problems. (c) 2021 Published by Elsevier Inc.